We are evaluating a project that costs $1,160,000, has a ten-year life, and has
ID: 2709179 • Letter: W
Question
We are evaluating a project that costs $1,160,000, has a ten-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 44,000 units per year. Price per unit is $45, variable cost per unit is $20, and fixed costs are $645,000 per year. The tax rate is 35 percent, and we require a 20 percent return on this project.
Calculate the accounting break-even point.
What is the degree of operating leverage at the accountin g break-even point? (Round your answer to 3 decimal places. (e.g., 32.161))
Calculate the base-case cash flow and NPV. (Round your NPV answer to 2 decimal places. (e.g., 32.16))
What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations and round your answer to 3 decimal places. (e.g., 32.161))
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We are evaluating a project that costs $1,160,000, has a ten-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 44,000 units per year. Price per unit is $45, variable cost per unit is $20, and fixed costs are $645,000 per year. The tax rate is 35 percent, and we require a 20 percent return on this project.
Explanation / Answer
a-1) BEP = Fixed Cost / (Price - Variable Cost)
Depreciaiton per year = 1,160,000/10 = $ 116,000
Fixed Cost per year = $ 645,000
Accounting Break Even Point = (645000 + 116000) / (45 - 20) = 30,440 units
a-2) DOL = 1 + (FC/OCF) = 1+ (FC / Dep) = 1 + (645000 / 116000)
= 1 + 5.560 = 6.560
b-1) Base Cash Flow = (P – VC)Q – FC](1 – T ) + Tax on Dep
= (45-20)44000 - 645000 (1-0.35) + 0.35 * 116000
=1100000 - 419250 + 40600 = $ 721,350
NPV = - Project Cost + OCF (i.e. Base Cash Flow)
= - 1,160,000 + 721,350 (PVIFA 20%,10yrs) = - 1,160,000 + 721,350 (4.1925) = - 1,160,000 + 3,024,259.875
= $ 1,864,259.88
b-2) In order to calculate sensitivity of NPV to sales, lets take a different quantity, say, 35000 and 40000 units
OCF at 35000 units = (45-20)35000 - 645000 (0.65) + 116000 (0.35) = 875000-419250+40600 = 496,350
OCF at 40000 units = (45-20)40000 - 645000 (0.65) + 116000 (0.35) = 1000000-419250+40600 = 621,350
NPV at 35000 units = -1,160,000 + 496,350 (4.1925) = 920,947.375
NPV at 40000 units = -1,160,000 + 621,350 (4.1925) = 1,445,009.875
So, sensitivity of NPV to sales = (920,947.375 - 1,445,009.875) / (35000-40000) = $ 104.813 per unit of sales
c) We have calculated OCF at variable cost of $ 20 earlier = $ 721,350
Lets calculate OCF as VC of $ 21 = (45-21)44000 - 645000 (1-0.35) + 0.35 * 116000
= 1056000 - 419250 + 40600 = $ 677,350
So, Change in OCF to change in VC = (721350 - 677350) / (20-21) = - $44000
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